商务与经济统计习题答案（第8版，中文版）SBE8-SM19

19-1Chapter19NonparametricMethodsLearningObjectives1.Learnthedifferencebetweenparametricandnonparametricmethods.2.Knowtheparticularadvantagesofnonparametricmethodsandwhentheyareandwhentheyarenotapplicable.3.Learnhowtousethesigntestfortheanalysisofpairedcomparisons.4.Beabletousethesigntesttoconducthypothesistestsaboutamedian.5.BeabletousetheWilcoxonsigned-ranktestandtheMann-Whitney-Wilcoxontesttodeterminewhetherornottwopopulationshavethesamedistribution.6.BeabletousetheKruskal-Wallistestsforthecomparisonofkpopulations.7.BeabletocomputetheSpearmanrankcorrelationcoefficientandtestforasignificantcorrelationbetweentwosetsofrankings.Chapter1919-2Solutions:1.BinomialProbabilitiesforn=10,p=.50.xProbabilityxProbability0.00106.20511.00987.11722.04398.04393.11729.00984.205110.00105.2461P(0)+P(1)=.0108;addingP(2),exceeds.025requiredinthetail.Therefore,rejectH0ifthenumberofplussignsislessthan2orgreaterthan8.Numberofplussignsis7.DonotrejectH0;concludethatthereisnoindicationthatadifferenceexists.2.Therearen=27casesinwhichavaluedifferentfrom150isobtained.Usethenormalapproximationwithµ=np=.5(27)=13.5and.25.25(27)2.6nUsex=22asthenumberofplussignsandobtainthefollowingteststatistic:2213.53.272.6xzWithwerejectifz2.33;sincez=3.272.33werejectH0.Conclusion:themedianisgreaterthan150.3.a.Letp=probabilitythesharesheldwillbeworthmoreafterthesplitH0:p.50Ha:p.50IfH0cannotberejected,thereisnoevidencetoconcludestocksplitscontinuetoaddvaluetostockholdings.b.Letxbethenumberofplussigns(increasesinvalue).Usethebinomialprobabilitytableswithn=18(therewere2tiesinthe20cases)P(x12)=.0482RejectH0ifthenumberof+signsisgreaterthan12.c.Withx=14,werejectH0.Theresultssupporttheconclusionthatstocksplitsarebeneficialforshareholders.NonparametricMethods19-34.Weneedtodeterminethenumberwhosaidbetterandthenumberwhosaidworse.Thesumofthetwoisthesamplesizeusedforthestudy.n=.34(1253)+.29(1253)=789.4Usethelargesampletestusingthenormaldistribution.Thismeansthevalueofn(n=789.4above)neednotbeinteger.Hence,µ=.5n=.5(789.4)=394.7.25.25(789.4)14.05nLetp=proportionofadultswhofeelchildrenwillhaveabetterfuture.H0:p.50Ha:p.50Withx=.34(1253)=426426394.72.2314.05xzWith=.05,werejectH0ifz1.645Sincez=2.231.645,werejectH0Conclusion:morethanhalfoftheadultsfeeltheirchildrenwillhaveabetterfuture.5.n=185+165=350µ=0.5n=0.5(350)=175.25.25(350)9.35nRejectH0ifz-1.96orifz1.961851751.079.35zDonotrejectH0;cannotconcludethereisadifferenceinpreferenceforthetwoshows.6.n=202+158=360µ=0.5n=0.5(360)=180.25.25(360)9.49nRejectH0ifz-1.96orifz1.962021802.329.49zChapter1919-4RejectH0;concludePackardBellandCompaqhavedifferentmarketshares.7.µ=0.5n=0.5(300)=150.25.25(300)8.66n1651501.738.66zp-value=2(.5000-.4582)=.0836DonotrejectH0;weareunabletoconcludethatthemedianannualincomediffers.8.µ=.5n=.5(150)=75.25.25(150)6.12nOnetailedtest:rejectH0ifz1.645For98+signs98753.766.12zRejectH0;concludethatahometeamadvantageexists.9.H0:Median15Ha:Median15Usebinomialprobabilitieswithn=8andp=.50:Onetailtestwith=.05,P(8+’s)=.0039P(7+’s)=.0312.0351P(6+’s)=.1094RejectH0if7or8+’s.With7+’sinthesample,rejectH0.Datadoesenableustoconcludethattherehasbeenanincreaseinthemediannumberofpart-timeemployees.10.H0:Median=152Ha:Median152µ=.5n=.5(225)=112.5.25.25(225)7.5nNonparametricMethods19-5RejectH0ifz-1.96orifz1.96For122cases122112.51.277.5zDonotrejectH0;weareunabletoconcludethatthemedianannualincomeneededdiffersfromthatreportedinthesurvey.11.n=50µ=0.5n=0.5(50)=25.25.25(50)3.54nRejectH0ifz1.64533hadwagesgreaterthan$58533252.263.54zRejectH0;concludethatthemedianweeklywageisgreaterthan$585.12.H0:ThepopulationsareidenticalHa:ThepopulationsarenotidenticalAdditive1Additive2DifferenceAbsoluteValueRankSignedRank20.1218.052.072.079+923.5621.771.791.797+722.0322.57-.54.543-319.1517.062.092.0910+1021.2321.22.01.011+124.7723.80.97.974+416.1617.20-1.041.045-518.5514.983.573.5712+1221.8720.031.841.848+824.2321.153.083.0811+1123.2122.78.43.432+225.0223.701.321.326+6Total62µT=0T(1)(21)12(13)(25)25.566nnnTTT6202.4325.5zChapter1919-6Two-tailedtest.RejectH0ifz-1.96orifz1.96Sincez=2.431.96werejectH0.Conclusion:thereisasignificantdifferenceintheadditives.13.WithoutRelaxantWithRelaxantDifferenceRankofAbsoluteDifferenceSignedRank151059912102332212101010811-36.5-6.510911175233810-23-310736.56.5141136.56.59636.56.5Total36µT=0T(1)(21)10(11)(21)19.6266nnnTTT361.8319.62zOne-tailedtest.RejectH0ifz1.645Sincez=1.831.645werejectH0.Conclusion:thereisasignificantdifferenceinfavoroftherelaxant.14.AirportDifferenceAbsoluteDifferenceSignedRankBostonLogan0.190.1910ChicagoMidway-0.020.02-3.5ChicagoO'Hare0.050.056Denver0.040.045FortLauderdale-0.010.01-1.5LosAngeles0.060.067Miami0.020.023.5NewYork(JFK)0.090.098OrangeCounty(CA)0.160.169Washington(Dulles)0.010.011.5T=45T(1)(21)10(11)(21)19.6266nnnNonparametricMethods19-7TTT4502.2919.62zRejectH0ifz-1.96orifz1.96.RejectH0;concludeadifferenceexistswithAvishigher.15.Service#1Service#2Differenc